February is crucial for Sam Allardyce's West Ham because they face home games against Swansea, Norwich and Southampton. Photograph: Ian Kington/AFP/Getty

If West Ham are looking for silver linings, there is always Tuesday's Capital One Cup semi-final against Manchester City to get excited about. Admittedly, West Ham are 6-0 down from the first leg but a cup semi-final is undoubtedly a grand occasion. Andy Carroll might get another run-out. Kevin Nolan will be back from his four-game ban. Upton Park will not be completely empty. Cup fever is building.

At least it will provide West Ham with some relief from their torrid league campaign and Sam Allardyce insists he will not select a weakened team against City. "We'll put a team together that tries to play for a bit of pride," he said.

But West Ham's pride has taken a sustained battering recently and Newcastle dished out the latest humiliation. Their smooth 3-1 victory sent West Ham back into the bottom three and although Allardyce was encouraged by the way his side fought back after an execrable first half, there could have been no complaints if Newcastle had scored five or six. Carroll and Carlton Cole both missed glaring chances to equalise for West Ham after Mike Williamson's own goal had given them hope but anything less than a Newcastle win would have been a travesty.

As ever, Allardyce's excuse was defensive injuries, with James Tomkins suspended and Winston Reid, Joey O'Brien, Guy Demel and George McCartney all injured. O'Brien, Demel and Tomkins could all return for the trip to Chelsea on 29 January – just as well, because West Ham's defence was a lumbering mess in their absence. Matt Taylor is not a right-back and Newcastle's Loïc Rémy could have outrun James Collins and Roger Johnson with his shoelaces tied together.

For Allardyce, the target is to win 22 points from West Ham's final 16 matches. Yet West Ham have never won successive games in the Premier League under Allardyce and four of their last six matches are against Arsenal, Liverpool, Manchester City and Tottenham. February may be a defining month; West Ham have home games against Swansea City, Norwich City and Southampton.

"The bottom line is 22 points out of 16 matches makes you safe," Allardyce said. "The key element lies in taking points from those around us in the table, not expecting to go and beat Chelsea. José [Mourinho] has never lost a Premier League game in the entire time he has been there [at home], so it would be an exaggerated opinion to say we are going to go there and win. The key games are against the ones around us – and having key players back."

The situation is exacerbated by West Ham's struggle in the transfer market. A deal to sign Monaco's Lacina Traoré on loan broke down at the 11th hour and the Ivory Coast forward had a medical at Everton on Sunday, which Allardyce described as "a real kick in the nuts". Newcastle delivered several more blows to West Ham's nether regions.

Yohan Cabaye, who scored two excellent goals, was allowed to do as he pleased by a West Ham midfield in which Mohamed Diamé's demeanour suggested he had somewhere better to be, and the Frenchman's performance demonstrated why Newcastle cannot afford to sell him this month.

By contrast, West Ham's Ravel Morrison looked distracted after the fuss caused by Fulham's attempts to sign him last week. "We'll let anybody go anywhere as long as they pay enough money," Allardyce said. It was not exactly a hands-off warning.

For Newcastle, the challenge is to find enough money to make Rémy's loan move from Queens Park Rangers permanent. The striker, who scored their second goal, has a £10m release clause in his contract but Alan Pardew said it is more complicated than Newcastle offering QPR that amount.

"We would like to do it permanent but there is a long way until that happens," Newcastle's manager said. "The player and his agents need to make sure that it is right for the player and we honour that. Obviously we are talking to him all the time."